[sr #3045] Support for pooled standard deviation for: Peak heights with partially replicated spectra -- June 19, 2013 - 14:50

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                 Summary: Support for pooled standard deviation for: Peak
heights with partially replicated spectra
                 Project: relax
            Submitted by: tlinnet
            Submitted on: Wed 19 Jun 2013 12:50:08 PM GMT
                Category: None
                Priority: 5 - Normal
                Severity: 3 - Normal
                  Status: None
                 Privacy: Public
             Assigned to: None
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
        Operating System: None

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Details:

According to the manual, 
http://www.nmr-relax.com/manual/spectrum_error_analysis.html, 
the variance for the replicated datasets are averaged, and used as the
variance for single replicated spectrum.

This is a very reasonable assumption, but I wonder if a pooled standard
deviation should be used instead.

If we look in the definition of IUPAC Gold Book:
http://goldbook.iupac.org/P04758.html

"""
Results from various series of measurements can be combined in the following
way to give a pooled relative standard deviation $s_{r,p}$:

$$
s_{r,p}=\sqrt{\frac{\sum(n_i-1)s_{r,i}^2}{\sum n_i -1}} =
\sqrt{\frac{\sum(n_i-1)s_i^2x_i^{-2}}{\sum n_i -1}}
$$
"""

It is not an easy subject, and the discussion can be "hot": See for example
these gals and gils: http://www.physicsforums.com/showthread.php?t=268377


So my question is, is the use of average of variances the right way to
estimate the variance for single recorded data point?
And should another way be implemented?




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